Deciphering the hydrogen-bonding scheme in the crystal structure of triphenylmethanol: a tribute to George Ferguson and co-workers

The disordered crystal structure of triphenylmethanol features tetrahedral chiral clusters formed through weak hydrogen bonds, leading to the formation of three-dimensional supramolecular motifs having left or right handedness.


Introduction
The hydroxy group is known as one of the most efficient nodes for the formation of hydrogen bonds, as a consequence of the polarization of the O-H bond, and also because it can behave both as donor and acceptor for building intra-or intermolecular bonds. In this context, the emblematic donoracceptor molecule is water, and many compounds have been crystallized as hydrates, in which the lattice water molecules contribute to a significant part of the crystal free energy (Batsanov, 2018); currently, almost 13% of the structures deposited in the Cambridge Structural Database are hydrates (CSD, Version 5.40, updated February 2019;Groom et al., 2016). The situation is a bit less favourable in the case of alcohols (RO-H), especially for tertiary alcohols having the hydroxy group surrounded by bulky hydrocarbon groups. For example, three hydrates for tert-butanol, (CH 3 ) 3 COH, have been successfully characterized [namely the dihydrate and heptahydrate (Mootz & Stä ben, 1993), and the decahydrate (Dobrzycki, 2018)], while tri-tert-butylmethanol, [(CH 3 ) 3 C] 3 -COH, has probably never been crystallized, although it has been studied in the solid state (Malarski, 1974). Although this ISSN 2053ISSN -2296 molecule is stable, it is not able to form stabilizing intermolecular O-HÁ Á ÁO hydrogen bonds, because of the steric hindrance of the three tert-butyl groups surrounding the OH donor group (Majerz & Natkaniec, 2006).
The case of triphenylmethanol, (C 6 H 5 ) 3 COH, should be intermediate between tert-butanol and tri-tert-butylmethanol, since it can be used as a clathrate host for methanol (Weber et al., 1989), and may be hydrogen bonded to a water molecule (Batisai et al., 2016), dimethyl sulfoxide, dimethylformamide (Eckardt et al., 1999) or Ph 3 P O (Steiner, 2000). Indeed, unsolvated triphenylmethanol can be easily crystallized from benzene or ethanol, affording large well-shaped clear colourless single crystals. However, these crystals are always weakly diffracting samples, as a consequence of a severe structural disorder (vide infra). The resulting ratio of observed to measured reflections is then quite low, which, in turn, makes the refinement very difficult. First attempts to refine a reasonable model failed (Weber et al., 1989), and it was only in 1992 that the crystal structure was published (Ferguson et al., 1992), based on room-temperature intensities measured on a CAD-4 diffractometer, with Mo K radiation. 2467 unique reflections were used, of which 41% were observed [I > 2.5(I)], and the structure was refined with a structural motif described as a 'hydrogen-bonded pyramidal tetramer which is disordered (71/29) about two interpenetrating sites'. The refinement was of limited accuracy and converged to R = 0.083 and wR = 0.068 with rigid idealized phenyl rings for all molecules, and isotropic atoms in the minor-disordered part of the asymmetric unit (253 variable parameters).
Although the structure reported by Ferguson et al. was incomplete, since hydroxy H atoms could not be located, the savoir-faire used by this team is quite impressive. They were able to solve and refine this challenging disordered structure, while others probably gave up by arguing that crystals were badly twinned. Above all, they did not attempt to over-interpret their data, and were aware that hydroxy H atoms were very imprecisely determined in their X-ray diffraction experiment. However, they indirectly recognized and described the presence of a weak hydrogen-bonding scheme, reflected in intermolecular OÁ Á ÁO contacts.
In 1999, Serrano-Gonzá lez et al. (1999) published a more elaborate article, focussed on the characterization of the hydrogen-bonding arrangement in triphenylmethanol, using neutron (T = 100 K) and X-ray diffraction data (T = 113 and  293 K), as well as solid-state 13 C NMR spectroscopy. A reliable structure based on neutron diffraction data was obtained, showing that each independent OH group has the H atom disordered over three sites. This model was then a suitable starting point for the refinement of X-ray structures, both at 113 and 293 K. Unfortunately, the final atomic coordinates were never deposited in the CSD, and there is no CIF available as supporting information. Fractional coordinates are tabulated, however, for X-ray refinements, H atoms are missing. Moreover, even using the favourable neutron scattering length for the protium nucleus, it was not possible to complete the structure. As stated in this article 'The hydroxy hydrogens of the minor tetramer could not be located from the difference Fourier map, and these hydrogen atoms were inserted in calculated positions based on those determined [ . . . ] for the major tetramer'.
We have now completed these works, using X-ray data collected at room temperature and low temperature with the Ag K radiation, revealing the accurate localization of the hydroxy H atoms in the disordered structure. A comprehensive insight into the hydrogen-bonding scheme that held together the tetrameric clusters is now afforded.

Refinements
Crystal data, data collection and structure refinement details are summarized in Table 1 for the two different crystals obtained from a single crystallization batch, but diffracted at different temperatures, i.e. 153 and 295 K. The disorder in the asymmetric unit was solved using the low-temperature data set, and all phenyl rings were restrained to be flat, with standard deviations of 0.1 Å 3 . Additionally, the phenyl rings in the minor part (molecules C and D) were restrained to have 1,3 distances similar to those in the corresponding rings of the disordered counterpart (molecules A and B), within standard deviations of 0.02 Å . H atoms in the phenyl rings were placed in idealized positions and refined as riding to their carrier C atoms, with U iso (H) = 1.2U eq (C). Hydroxy H atoms were (Left) Difference electron-density map computed using low-temperature data, after refining the full disordered model but omitting hydroxy H atoms. Grey molecules correspond to the main part A/B (occupancy 0.74) and gold molecules to the minor part C/D (occupancy 0.26); hydroxy O atoms are represented with magenta ellipsoids. Two tetramers are displayed in a projection along the threefold crystallographic axis. The difference map is plotted at the 0.33 e Å À3 level (green wire for Á > 0 and red wire for Á < 0; Dolomanov et al., 2009). Note how most of the positive residuals are concentrated within the cavity delimited by the eight clustered O atoms. The inset is the crystal used for data collection. Note the triangular face on the top of the crystal, corresponding to the (003) face. (Right) Final model, including 24 disordered hydroxy H atoms, shown as green spheres with a radius corresponding to 33% of the van der Waals radius. All C and O atoms are displayed with displacement ellipsoids at the 20% probability level (Mercury; Macrae et al., 2008). found in a difference map (Fig. 2, left) and refined with U iso (H) = 1.5U eq (O). Atoms H1A and H1C are disordered by symmetry, and their site occupancies were fixed as one-third of the occupancy of the part to which they belong. The hydroxy H atoms for molecules in general positions are disordered over sites H1BA, H1BB and H1BC for molecule B, and H1DA, H1DB and H1DC for molecule D, and the occupancy for each site was also fixed as one-third of the occupancy of the part to which it belongs. The geometry of the C-O-H groups was first restrained to a sensible target, by restraining distances to O-H = 0.85 (1) Å and CÁ Á ÁH = 1.93 (2) Å in molecules A and C; for molecules B and D, the applied restraints were O-H = d, HÁ Á ÁH = (8/3) 1/2 Â d and CÁ Á ÁH = 2.27 Â d, where d is a common free variable. Standard deviations for these restraints were 0.02, 0.03 and 0.03 Å , respectively. After convergence, the positions of all hydroxy H atoms were fixed, and these atoms were refined as riding on their carrier O atoms. The final model for the complete structure at 153 K was refined against data collected at 295 K, with an extra restraint: in the minor-disordered part (molecules C and D), rigid-bond restraints were applied with standard deviations of 0.004 Å for the 1,2 and 1,3 distances (Thorn et al., 2012;Sheldrick, 2015b).

Results and discussion
The asymmetric unit of the trigonal cell includes two disordered parts with site-occupancy factors converging at 153 K  Hydrogen-bonding schemes in the tetramer formed by A/B molecules. The top figure shows the arrangement of the four molecules and the 12 hydroxy H-atom sites. The left and right panels represent right-( sup R) and left-handed ( sup S) supramolecular clusters, respectively. The first figure is oriented down the crystallographic threefold axis and the other is oriented down a noncrystallographic threefold axis. Each cluster comprises six hydrogen bonds (dashed gold bonds), involving six H-atom sites (pink H atoms). Topological graphs G(4,6) for supramolecular clusters based on O-HÁ Á ÁO hydrogen bonds are represented in the centre. Nodes are represented as red balls (O atoms). Arrows forming a ring R d a (n) are stacked over O-H covalent bonds and oriented in the direction d!a, where d is the donor and a the acceptor for a hydrogen bond. Arrows involved in a ring are shown in bold, while those not participating in a ring are greyed out. Polygons delimited by R rings in the 2-space are coloured yellow and blue for sup R and sup S clusters, respectively, and rings in the projection plane are read clockwise in all cases. For the first-level graphs, Re stands for Rectus and Si for Sinister. Note that all figures on the left are mirror images of the figures on the right, including descriptors of the R rings. towards 0.7436 (17) (molecules A and B hereafter) and 0.2564 (17) (molecules C and D hereafter), close to the occupancies reported by Ferguson et al. of 0.71 and 0.29. Each part contains two independent molecules, one of which has the C-O bond lying on the threefold axis in the space group R3, while the other is located in a general position. The arrangement of these four disordered molecules generates overlapped phenyl rings in the asymmetric unit, making the refinement of displacement parameters a tedious task (see x2.2). However, the molecular structure based on data collected at 153 K can be considered as satisfactory, although the refinement was carried out with restrained geometry for the phenyl rings. The refinement based on data collected at 295 K is not as easy, since the scattering power of the crystal decreases dramatically: the fraction of observed data [I/(I) > 2] drops from 50% at 153 K to 36% at 295 K. However, the structure is essentially unmodified, and occupancies for the disordered parts refined to 0.761 (3) and 0.239 (3). At both temperatures, all non-H atoms could be refined anisotropically (see Fig. 2, right), after which phenyl H atoms were placed in idealized positions.
The localization of the hydroxy H atoms was far more complex. A difference map using room-temperature data is useless, in contrast to the map computed with data collected at low temperature. At 153 K, most of the positive residuals are found close to the O atoms (Fig. 2, left), allowing the determination of sensible coordinates for H atoms disordered by symmetry (H1A and H1C for molecules A and C in special positions). At this point, the highest residuals are found close to O1B, forming a tetrahedral geometry with O1B; although molecule B is located in a general position, the O-H group emulates the disorder imposed by symmetry in molecule A (see top inset in Fig. 3). The same situation is repeated for molecule D, with much smaller residuals because this molecule belongs to the minor part of the disordered asymmetric unit. Ultimately, all the molecules in the crystal have their hydroxy H atoms disordered over three sites, and once the asymmetric unit is expanded to tetramers, eight independent molecules are clustered in such a way that the cavity delimited by eight O atoms is filled with 24 sites for disordered hydroxy H atoms (Fig. 2, right). Each C-O-H group can also be seen as a rigid group rotating about its C-O axis, producing for the H atom an electron density smeared out over a ring; nevertheless, the free rotation should be hindered through the formation of weak hydrogen bonds (Schrö der et al., 2004). Such a description would be consistent with 2 H NMR spectroscopy experiments carried out on Ph 3 COD, showing that each hydroxy group is dynamic by rotation about the C-OD bond, on the 10 À3 to 10 À8 s time scale (Aliev et al., 1998).
All OH groups behave as donor groups for intermolecular O-HÁ Á ÁO hydrogen bonds. For the main part A/B, with occupancy = 0.74, three B molecules placed close to the threefold axis are connected to form an R 3 3 (6) ring, corresponding to a first-level graph with H1BB as donor (Table 2, entry 3). This motif is repeated with H1BC (Table 2, entry 4), however, if the crystal orientation is preserved, this ring motif is enantiomorphic with the previous one. Finally, the third disordered site for the hydroxy H atom, H1BA, is engaged in a second-level graph with O1A as acceptor (Table 2, entry 2), giving a ring motif R 2 3 (6). Site O1A also serves as a donor, forming three symmetry-equivalent O1A-H1AÁ Á ÁO1B hydro-  Table 2 Hydrogen-bond geometry (Å , ) for the 153 K data. Symmetry codes: (i) Ày þ 1; x À y; z; (ii) Àx þ y þ 1; Àx þ 1; z.

Figure 4
Complete set of hydrogen bonds, represented as dashed lines, in the tetramer formed by molecules A and B (left), and in the tetramer formed by molecules C and D (right). Figures are oriented down the crystallographic threefold axis. Labels (1)Á Á Á(8) on hydrogen bonds indicate the entry in Table 2. Each cluster has four independent bonds, affording 12 bonds for the tetramer, consistent with the C 3 point symmetry of the tetramer. These figures can be compared to the model published in 1999 (see Fig. 4 in Serrano-Gonzá lez et al., 1999).
gen bonds ( Table 2, entry 1), and is involved in the largest rings, R 3 4 (8). All rings are depicted in Fig. 3, along with schematic representations of the corresponding graphs and their pathways [i.e. the constructor graphs and the qualitative descriptors, in the terminology coined by Motherwell et al. (1999)].
The tetramer based on A and B molecules includes 12 hydrogen bonds. Each disordered hydroxy H atom is engaged in a single hydrogen bond, and each O atom serves three times as acceptor (Fig. 4, left). The hydrogen-bonded supramolecular cluster formed in the tetramer is associated with a topological graph embedded in 3-space, i.e. G(4,6) = [R 3 3 (6)-R 3 4 (8)R 2 3 (6)], for which the faces are the R(n) rings described in Fig. 3. In the parlance of graph theory, the finite directed graph G(4,6) based on the 'pyramidal tetramer' mentioned by Ferguson et al. is regular, complete and intrinsically chiral (Flapan, 1995). The four nodes for G(4,6) are provided by four molecules (or four hydroxy O atoms for simplicity) and the six arrows are oriented O-HÁ Á ÁO hydrogen bonds, the tail of the arrow being the donor OH group and the head being the acceptor O atom. It is noteworthy that for each right-handed R(n) ring, there is one related left-handed ring, as illustrated in Fig. 3. For example, in the first-level R 3 3 (6) subgraph embedded in the 2-space, arrows rotate clockwise around the crystallographic threefold axis for the ring including arrows O1B-H1BBÁ Á ÁO1B (Rectus face for topological graph G), and anticlockwise for the ring including arrows O1B-H1BCÁ Á ÁO1B (Sinister face for topological graph G).
A topologically isomorphous graph G 0 (4,6) can be built with the minor part of the asymmetric unit, including hydrogen bonds similar to those described for the main tetramer, although the relative positions of the 12 H-atom sites is modified through a small rotation around the C1C-O1C axis (Fig. 4, right). Therefore, the mixture of eight molecules built on the asymmetric unit, as represented in Fig. 2, affords a racemic mixture of supramolecular enantiomorphic tetramers sup R and sup S built on 24 hydrogen bonds. Obviously, the molecules themselves are achiral, but the supramolecular chirality results from the asymmetric configuration of the hydrogen bonds (Sasaki et al., 2014). Neither the unit cell nor the crystal are chiral objects, since the molecule crystallizes in a centrosymmetric space group, R3.
The set of 24 hydrogen bonds depicted in Fig. 4 comprises only weak hydrogen bonds, with HÁ Á ÁO separations in the range 2.21-2.38 Å and O-HÁ Á ÁO angles far from linearity, in the range 121.4-138.2 , at 153 K. The refinement using roomtemperature data indicates that the supramolecular chiral clusters are retained, although hydrogen bonds are slightly weakened by ca 0.06 Å for HÁ Á ÁO separations (compare Tables 2 and 3). These geometric parameters were compared with those found in other supramolecular networks formed in the crystalline state by tertiary alcohols, using the methodology developed at the CCDC (Wood et al., 2009). Parameters for intermolecular O-HÁ Á ÁO contacts in tertiary alcohols were retrieved from the current release of the CSD, omitting disordered, polymeric and ionic structures. Hydroxy H-atom positions were normalized within ConQuest to O-H = 0.993 Å , in order to avoid systematic errors in contact distances (Bruno et al., 2002). The search was limited to organic compounds not flagged with errors, and reported with R 1 < 0.075, affording 1215 hits, corresponding to 1812 raw data (d, ), where d is the HÁ Á ÁO distance and is the O-HÁ Á ÁO angle. Only contacts with d shorter than the van der Waals (vdW) distance were retained [r vdW (H) + r vdW (O) = 2.72 Å ; Bondi, 1964]. Data were converted into spherical polar coordinates (x, y), where x = (d/2.72) 3 and y = 1 À cos (180 À ), Histogram of the O-HÁ Á ÁO intermolecular hydrogen-bond geometry in the crystal structures of tertiary alcohols, in spherical polar coordinates (x, y), with the CSD frequency shown in the third dimension (OriginLab, 2012). A log 10 rainbow colour scheme is used to highlight small frequencies. Some values for the O-HÁ Á ÁO angles are reported on axis y, for reference. Note the similarity of the distribution with that depicted in the CCDC article about the directionality of hydrogen bonds (Wood et al., 2009;see Fig. 2 in this article). The green patch marked with an arrow in the (x, y) plane defines the area for hydrogen bonds in the A/B tetrameric cluster of the title compound at 153 K. The inset shows the Hirshfeld surface mapped over d (À1 to 1 Å ) for the A/B molecules at 153 K (Turner et al., 2017); each of the four red patches on the surface is related to a single node for the topological graph G(4,6) of the A/B tetramer (see Fig. 3). Table 3 Hydrogen-bond geometry (Å , ) for the 295 K data. assuming that d and are expressed in Å and , respectively (Lommerse et al., 1996). Outside these well-defined territories, the observed frequency collapses. Interestingly, the title compound displays O-HÁ Á ÁO contacts on the borderline between truly hydrogen-bonded alcohols and the near-zero frequency area (see green patch on the ground level in Fig. 5). However, although of very limited strength, hydrogen bonds in the tetramers depicted in Fig. 3 are genuinely present, as reflected in the Hirshfeld surface for any pair of molecules involved in a tetrameric supramolecular cluster (Fig. 5, inset). In other words, triphenylmethanol could represent the boundary between hydrogen-bonded and nonhydrogen-bonded tertiary alcohols. This also opens the possibility that a phase transition occurs for triphenylmethanol somewhere between T = 293 and 433 K (melting point), if thermal energy kT is able to dismantle the network of weak hydrogen bonds.
In order to evaluate the stability of the noncovalent bonds in this crystal, George Ferguson and co-workers came across a more chemical strategy, by determining the crystal structures of molecules isoelectronic with triphenylmethanol . Their hypothesis was that 'with only modest changes in the steric demands at the unique central C atom, while keeping the number of hydrogen-bond donors and acceptors unchanged, the patterns of hydrogen bonding can be altered drastically'. Indeed, diphenyl(pyridin-4-yl)methanol has a simple achiral supramolecular structure based on C(7) chains. For triphenylmethanamine, two polymorphic forms have been described: the orthorhombic phase does not form hydrogen bonds at all , while the triclinic phase features dimers through the formation of N-HÁ Á ÁN hydrogen bonds, due to the statistical disordering of the amino H atoms (Khrustalev et al., 2009;Schulz et al., 2013). The NH 2 group then displays a geometry reminiscent of that of the OH groups in triphenylmethanol. However, no chiral supramolecular clusters are formed with the amine, and the asymmetric unit includes a single nondisordered molecule. A rhombohedral polymorph for this amine has also been deposited recently; unfortunately, after inspection of this structure, it turns out that the formula is wrong: the diffracted crystal was almost certainly triphenylmethanol (Bagchi et al., 2014; R3 space group, T = 298 K, R 1 = 10%). In the opposite direction, strong O-HÁ Á ÁO hydrogen bonds can be restored in sterically hindered tertiary alcohols by just adding a methylene group: in the crystal structure of triphenylethanol, Ph 3 CCH 2 OH (nondisordered P2 1 /c crystal, Z 0 = 2; , molecules aggregate into discrete achiral R 4 4 (8) rings. In comparison with triphenylmethanol, the prochiral character of the supramolecular structure is lost, and the compound lies within a sharp peak of 'normal' crystal structures in a (x, y) distribution similar to that depicted for tertiary alcohols in Fig. 5.